Alloy nanoparticles can exhibit several different structures due to segregation and phase separation. In the case of an alloy with a tendency to phase separate, the core-shell (CS) configuration and the so-called "Janus" one are the most commonly observed configurations. For a given alloy, the relative stability of these configurations depends on the size of the particle, the temperature, and the chemical composition. Using canonical Monte Carlo simulation on a rigid lattice, we study the stability diagram of bimetallic nanowires and its evolution as a function of the length of nanowires. We consider successively alloys with a weak and strong superficial segregation tendency. The simplicity of this 1D system allows us to extract the pertinent energetic parameters that control the relative stabilities. Furthermore, we find that the critical temperature decreases when increasing the size of the system. Phase diagrams and stability diagrams are compared and discussed in terms of the behavior of an assembly in mutual equilibrium with each other or of an assembly of isolated nanoparticles.